# NxDWS - Calculates the Downside Deviation

Returns the downside deviation of a given data set.

## Syntax

NxDWS(X,M)

X
is the portfolio simple rate of returns data series (a one-dimensional array of cells (e.g., rows or columns)).
M
is the minimum acceptable return (MAR). If missing, a zero (0) value is assumed.

#### Status

The NxDWS function is available starting with NumXL version 1.68 CAMEL.

## Remarks

1. The downside deviation (DWS) is a measure of downside risk that focuses on returns that fall below a minimum threshold or minimum acceptable return (MAR).
2. The DWS is an indicator used to assess the relative riskiness of one investment fund or strategy versus another.
3. By definition, all values in the input data set (i.e., X) must be greater than -1.0.
4. The input data series may include missing values (e.g., #N/A, #VALUE!, #NUM!, empty cell), but they will not be included in the calculations.
5. The DWS is computed as follows:

$$\textrm{DWS}= \sqrt{\frac{\sum_{i=1}^{N}{G(r_i)}}{N}}$$
$$G(r_i)=\left\{\begin{matrix} (r_i-r_m)^2 & r_i<r_m\\ 0 & ri \geqslant r_m \end{matrix}\right.$$
Where:
• $N$ is the number of data points with non-missing values.
• $r_i$ is the simple return for the i-th data point.
• $r_m$ is the minimum acceptable return (MAR).

## Examples

Example 1:

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A B
Date Data
1/1/2017 #N/A
2/1/2017 0.030
3/1/2017 0.020
4/1/2017 -0.007
5/1/2017 0.055
6/1/2017 0.028
7/1/2017 0.002
8/1/2017 -0.117
9/1/2017 0.012
10/1/2017 0.021
11/1/2017 0.111

Formula Description (Result)
=NxDWS(\$B\$2:\$B\$14,0.01) DWS (0.023535)